See appendix.

From (REF ), we have that the perturbation bound is determined by the ratio between the target rank \(n\)  and the oversampling parameter \(l\) . The error is large if \(l\)  is small. In practice, it is sufficient to use \(l=5\)  or \(l=10\) . And there is rarely any advantage to select \(l>10\)  [1]}. In addition, from (REF ), we know that the bound will decrease if we increase the power parameter \(q\) . The effect of \(l\)  in terms of running time and realization error is studied further in Section V where we observe that the stochastic Ho-Kalman algorithm is robust to the choice of \(l\) .
In case the average perturbation as characterized by Lemma REF  doesn't feel like a helpful quantity, a deterministic error bound is also achievable:
